Teacher: In this task, you are given a second sentence. Your task is to generate the first sentence on the same topic but incoherent and inconsistent with the second sentence.
Teacher: Now, understand the problem? If you are still confused, see the following example:
Additionally , they donated US $200,000 to the All Souls Hospital in Morristown , New Jersey , US $100,000 of which were donated specifically by his wife .
Solution: They also supported an all girls ' school in Saint - Briac - sur - Mer , Brittany , France .
Reason: Given a coherent sentence, an incoherent previous sentence to the given sentence is generated with the same topic of the given sentence

Now, solve this instance: Therefore , the remainder of this article will be restricted to the quotients of polynomial rings by ideals .
Student:
Thus , the graded algebras generated by elements of degree 1 are exactly , up to an isomorphism , the quotients of polynomial rings by homogeneous ideals .